Artificial intelligence systems frequently group like elements of element pairs to establish relationships among elements. By establishing relationships among elements, these systems are able to improve system performance. For example, in semiotic decision-making systems, element pairs such as pairs of letters or words are processed to create sets of letters or words to improve performance characteristics such as processing speed and accuracy. An exemplary semiotic decision-making system in which letter element pairs are grouped into sets of letters is described in U.S. Pat. No. 6,275,817 to Reed et al. entitled SEMIOTIC DECISION MAKING SYSTEM USED FOR RESPONDING TO NATURAL LANGUAGE QUERIES AND OTHER PURPOSES AND COMPONENTS THEREFOR, which issued as a patent on Aug. 14, 2001.
There is an ever-present desire for artificial intelligence systems having higher speed and accuracy. Although improvements in accuracy are achievable by grouping like elements of element pairs, the grouping process is computationally intensive, which can adversely affect speed. Accordingly, improved methods and apparatus are needed for efficiently grouping like elements of element pairs that are not subject to this limitation. The present invention addresses this need among others.